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An airplane goes over antartica. According to a passenger who always faces towards the front of the airplane, which side of the wing has a higher electric potential (right or left)?

I realise this question can be answered in terms of free electrons having a velocity and solving for the lorentz force. And in this case the right wing always has a higher potential.

But I vaguely remember other sources (I've been looking for them) solving this problem as if the airplane's wings were some sort of conducting loop of wire. If this is so, then what's the rationale here? I don't see how it is a loop of conducting wire.

Thanks.

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Airplane wings typically have discharging brushes attached to them so that they can exchange charge with the environment.

Charge that builds up on the wing is exchanged for example with water vapor in the air. In this sense, it's a "loop" because the environment closes the circuit.

See for example this patent: http://www.google.com/patents/US3585447

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  • $\begingroup$ If I'm visualising this correctly, then there wouldn't be an induced emf close to the poles since $\theta=90$ $\endgroup$
    – DLV
    Nov 20, 2014 at 3:34
  • $\begingroup$ You are talking about net charge buildup due to air friction, and the corona discharge (St Elmer's fire, I think it's called). It seems to me this question is about something different - emf due to electrons moving in a magnetic field. $\endgroup$
    – Floris
    Nov 20, 2014 at 4:07
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    $\begingroup$ @floris charge build up due to any phenomenon. Simply providing a reason why there would be a loop involved in the calculation, because that's what was asked. $\endgroup$ Nov 20, 2014 at 5:36
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The "loop" might refer to the eddy current effect that large metal objects experience when moving into a changing magnetic field - current will flow to counter the change in flux. An excellent picture can be found [source]:

enter image description here

This effect can be quite spectacular: if you drop a strong magnet down a thick copper tube, it will almost appear to levitate, for example. This shows that with strong fields and rapid changes, the effect is very real.

But when you are flying near the South Pole there is very little change in flux, therefore no eddy currents. If there is any effect at all it would indeed be the net velocity of the electrons experiencing a force due to the (static) magnetic field.

You need to draw a careful picture to figure out if the force is pointing to the left or right - and recognize that an electron moving left means the highest potential is on the right. Also - the South Pole has field lines coming out of it (it is a "magnetic north pole"), but I assume you know that.

Incidentally, related to this is the Hall effect: in a Hall sensor, the velocity of the charge carriers is induced with a current, and a voltage is observed perpendicular to both the current and the magnetic field. What is fascinating is the fact that p-doped semiconductors will exhibit the opposite voltage from n-doped ones - positive charge moving one way or negative charge moving the other way experience a force towards the same side of the sensor, but result in opposite polarity of the signal. This is a beautiful demonstration of the fact that "holes" (which look like negative charge moving in the opposite direction) really are positive charges moving. Very unintuitive.

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  • $\begingroup$ Whoa. Didn't know these things existed, thanks for this answer! $\endgroup$
    – DLV
    Nov 20, 2014 at 4:47

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